Momentum Momentum Impulse Problems Physics 1D03 - Lecture 25

Definition: The linear momentum p of a particle is its mass times its velocity: p  mv Momentum is a vector, since velocity is a vector. Units: kg m/s Physics 1D03 - Lecture 25

Impulse , or dp = F dt Newton #2: For a constant force, Dp = F Dt . The vector quantity F Dt is called the Impulse: J = FΔt = Δp (change in p) = (total impulse from external forces) (Newton’s Second Law again) (Extra) In general (force not constant), we integrate: where the integral gives the area under a curve… Physics 1D03 - Lecture 25

Area = t t Impulse is the area under the curve. The average force is the constant force which would give the same impulse. Compare with work: W = F Dx ; so the work-energy theorem (derived from Newton #2) is DK = F Dx. Physics 1D03 - Lecture 25

Example A golf ball is launched with a velocity of 44 m/s. The ball has a mass of 50g. Determine the average force on the ball during the collision with the club, if the collision lasted 0.01 s. Physics 1D03 - Lecture 25

Example Use the impulse-momentum theorem to find how long a falling object takes to increase its speed from 5.5m/s to 10.4m/s. Physics 1D03 - Lecture 25

Example A 150 g baseball is thrown with a speed of 20m/s. It is hit straight back toward the pitcher at a speed of 40m/s. The interaction force is shown by the graph: What is the maximum force Fmax that the bat exerts on the ball ? Fmax Physics 1D03 - Lecture 25

Example: the fire extinguisher How can we calculate the backwards force a fire extinguisher exerts on the operator? gas Plan: Calculate the momentum transferred to the gas in an arbitrary time Dt; this is equal to the impulse the gas gets from the extinguisher nozzle. From Newton’s Third Law, the nozzle gets an equal but opposite impulse (somehow) from the gas. Since impulse is FDt, divide by Dt to get the force. Result: F = (speed of gas) x (mass of gas ejected per unit time) Physics 1D03 - Lecture 25

Concept Quiz A 100g rubber and a 100g clay ball are thrown at a wall with equal speed. The rubber ball bounces back while the clay ball sticks to the wall. Which ball exerts a larger impulse on the wall ? the clay bass b/c it sticks the rubber ball b/c it bounces they are equal because the have equal momenta neither exerts an impulse b/c the wall doesn’t move Physics 1D03 - Lecture 25